Not applicable.
(1) Field of the Invention
The present invention relates to systems and methods for processing acoustic signals and particularly, to a system and method for processing an underwater acoustic signal by identifying nonlinearity (e.g., chaos) in the underwater signal.
(2) Description of the Prior Art
Underwater acoustic signals, such as sonar signals, have intrinsic nonlinear properties. Nonlinearity is a property of a dynamical system whereby the evolution of its variables depends on products of two or more of the present values of the variables. Chaos is a special type of nonlinearity. A defining characteristic for chaos to be present in a nonlinear system is that the system contains at least one positive lyapunov exponent. Nonlinearity in acoustics can arise from irregular (i.e., nonlinear) boundary conditions of the propagation channel, the target xe2x80x9cechoxe2x80x9d response, reverberant scattering within the channel, or any combinations of these.
Underwater acoustic sensors and sonar systems typically employ traditional linear processing methods. The intrinsic nonlinear properties present in underwater sound propagation and reflection cannot be detected using the traditional linear processing techniques. A linear processor can detect first order effects only. Linear processes are additive processes, i.e., the additive property of superposition applies only to linear processes. For nonlinear processes, the superposition principle no longer holds up and one must revert to some alternate means of signal analysis to best determine the information contained in the signal. Although a conventional method of signal analysis, such as a Fourier analysis, is very robust for analysis of a signal for a linear process, such methods are unable to make quantitative delineations in a signal structure whenever there exists a dominant nonlinearity in the signal of interest. Thus, the nonlinearity and chaos in the acoustic signature cannot be exploited when using conventional linear processing systems and methods.
Accordingly, one object of the present invention is to process an underwater acoustic signal by identifying nonlinearity (i.e., chaos) in the underwater acoustic signal.
In accordance with one aspect of the present invention, the system and method of the present invention detects the underwater acoustic signal and digitizes the underwater acoustic signal to produce an acoustic time series representing the underwater acoustic signal. The acoustic time series is reconstructed using a phase space embedding algorithm to generate a phase space embedded acoustic signal. A differential radius signal is generated from the phase space embedded acoustic signal using chaotic radius computations and differential computations. Thresholds detected in the differential radius signal represent nonlinear events hidden in the underwater acoustic signal.
According to one embodiment of the system and method, the phase space embedding algorithm is:
Y(t)={S(n), S(n+T), S(n+2T), . . . S(n+(mxe2x88x921)T)]
where S(n) represents the acoustic time series for n=1,2, . . . N, T is a time shift parameter, m is the number of dimensions in the embedding space, and Y(t) is a time dependent Euclidean vector function in Rm. The dimension m can be determined using a False Nearest neighbor (FNN) technique. The time shift parameter T can be determined by computing average mutual information (AMI) or by selective choice from a number of trial values for T.
In accordance with another aspect of the present invention, a nonlinear signal processor processes the acoustic time series representing the underwater acoustic signal. The nonlinear signal processor comprises a phase space embedded signal generator for reconstructing the acoustic time series using a phase space embedding algorithm to generate a phase space embedded acoustic signal. A chaotic radius processor computes a chaotic radius for each point in phase space for the phase space embedded acoustic signal producing a time series of chaotic radius values. A differential radius processor computes a time derivative of the time series of chaotic radius values to produce the differential radius signal.